L'endoscopie tordue n'est past si tordue

The author considers the fundamental lemma for twisted endoscopy, for the units of Hecke algebras only.

He proves that it is true if two other lemmas are true: the fundamental lemma for Lie algebras (and non-twisted endoscopy) and another lemma called ""non-standard fundamental lemma"".

This lemma assert equality between stable orbital integrals on the Lie algebras of two groups as a symplectic group and an odd special orthogonal group of the same rank.

A similar result is proved for transfer conjecture.